Q. 20 Compute聽the聽divergence聽of聽th... [FREE SOLUTION]

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Chapter 14: Q. 20 (page 1132)

$Compute the divergence of the vector fields in Exercises 17 鈥� 22 . G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k$

Short Answer

Expert verified

$div G = = 2 x - 2 cosz + 2 {ze}^{x^{2} + y^{2} + z^{2}}$

Step by step solution

Step 1. Given information is:

$G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k$

Step 2. Divergence of vector field

$If G (x, y, z) = g_{1} (x, y, z) i + g_{2} (x, y, z) j + g_{3} (x, y, z) k, then div G = \frac{鈭� g_{1}}{鈭� x} + \frac{鈭� g_{2}}{鈭� y} + \frac{鈭� g_{3}}{鈭� z} Here, G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k Compare this with, G (x, y, z) = g_{1} (x, y, z) i + g_{2} (x, y, z) j + g_{3} (x, y, z) k Then, g_{1} (x, y, z) = x^{2} + y 鈭� z, g_{2} (x, y, z) = 鈭� 2 y \cos z, g_{3} (x, y, z) = e^{x^{2} + y^{2} + z^{2}} div G = \frac{鈭� g_{1}}{鈭� x} + \frac{鈭� g_{2}}{鈭� y} + \frac{鈭� g_{3}}{鈭� z} = \frac{鈭� (x^{2} + y 鈭� z)}{鈭� x} + \frac{鈭� (鈭� 2 y \cos z)}{鈭� y} + \frac{鈭� (e^{x^{2} + y^{2} + z^{2}})}{鈭� z} = 2 x - 2 \cos z + 2 z e^{x^{2} + y^{2} + z^{2}}$

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91影视

$Compute the divergence of the vector fields in Exercises 17 鈥� 22 . G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Divergence of vector field

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ComputethedivergenceofthevectorfieldsinExercises17鈥�22.G(x,y,z)=(x2+y鈭�z)i鈭�2ycoszj+ex2+y2+z2k

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Divergence of vector field

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Decision Maths

Calculus

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

$Compute the divergence of the vector fields in Exercises 17 鈥� 22 . G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k$